I feel like they have mutual respect for each other even if they disagree with and don't understand why the other goes about things the way they do. I feel like Cross would trust Komui with Allen and the 14th's fate more than he would almost anyone else... but that's not to say that he would trust him enough to tell him things. Just that he believes he and Komui have the same goal and that Komui would do the right thing even without all Cross' secret information.
Same question I'm asking everyone, I give you control over the 8 slots of my muse list, who stays, who gets cut and who do you replace the cut ones with? :D